
where \((\Omega _1, \ldots , \Omega _7)\)  and two additional 1-forms \((\Omega _8, \Omega _9)\)  together define a rank 14 principal bundle over the 5-manifold \(M\)  (see [1]} and Section 5 of [2]}). A representative metric in Nurowski's conformal class [2]} is given by
\(g=2 \theta _1 \theta _5-2\theta _2 \theta _4+\frac{4}{3}\theta _3 \theta _3.\) 
